Let D be the unit disk D = {(x, y) | x² + y² ≤ π }. Calculate ə Ə ₁ ( [xsin (2² + y²³)] - [3² sin(x² + y²)]) dA. ду ;

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

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Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

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Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

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Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: 1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate…

A: We are Given that : z1=1+iz2=-1+i ⇒z1+z2=(1+i)+(-1+i)=2i and  ⇒z1-z2=(1+i)-(-1+i)=1+i+1-i=2

Q: Compute (47 SK) - dA, where s is the square of side length 3 perpendicular to the e-axis, centered…

A: According to question given that∫S(4i→+5k→).dA→Where S is the square of  the side length  3…

Q: In each case, determine if ₁ and ₂ are parallel, perpendicular, or neither. Explain. a) ₁: 4x-6y=9…

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Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

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Q: Prove that the angle between the tangents from (a, ß) to the circle x² + y² = a² is 2tan ¹(a/√S),…

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Q: The figure satisfies the Midpoint theorem for a triangle. Calculate (x + y) 4у x + 4 6(у-1) 4x -2

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

Q: Let u = 2i - j, v = 4i + j, and w = i + 5j. Find specified scalar u . v + u . w.

A: We will apply dot product of vectors.

Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: Let ä(t) = (5, 4, 2)t + (-6, -4,1) and (u) = (-2, 1, 2)u+ (2, -8,-6). Find the acute angle between…

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Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…